Download 13 Index notation, BIDMAS and further factorising

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Unit 2 | 13 Index notation, BIDMAS and further factorising | Student Book chapter 8
13 Index notation, BIDMAS and further factorising
BIDMAS
F
Work out:
a 63713
b 30 2 5 3 2
c 12 4 (4 1 2)
a 6 3 7 1 3 5 42 1 3 5 45
Multiplication comes before Addition in BIDMAS.
b 30 2 5 3 2 5 30 2 10 5 20
Multiplication must be done BEFORE Subtraction.
c 12 4 (4 1 2) 5 12 4 6 5 2
Brackets must be done first. Then the Division
can be done.
Working with powers
C
Simplify these expressions by writing as a single power:
a 53 3 54 4 52
b 3x5y 3 5x3y7
When multiplying, ADD the powers;
when dividing, SUBTRACT the powers.
a 53 3 54 4 52 5 53 1 4 — 2 5 55
First rearrange as shown: numbers
then x terms then y terms.
b 3x5y 3 5x3y7 5 3 3 5 3 x513 3 y117
It is a common
error NOT to
cube the 2 as
well, giving 6x3.
c (2x)3
5 15x y
8 8
Now use the rules for indices.
c (2x)3 5 2x 3 2x 3 2x 5 8x3
Cubing means repeat the bracket
three times and multiply.
Expanding brackets
Expand:
a 3x(2x 1 1)
b 7x(8x 2 3y)
a 3x(2x 1 1) 5 3x 3 2x 1 3x 3 1 5 6x2 1 3x
b 7x(8x 2 3y) 5 56x2 2 21xy
Do not forget to multiply
BOTH terms by 3x.
Multiply each term by the 7 AND the x.
Expanding and simplifying
Expand and simplify 5(4x 1 y) 2 2(3x 2 2y)
Remember that a MINUS outside the
bracket changes the sign inside it.
5 20x 1 5y 2 6x 1 4y
5 14x 1 9y
First do 20x 2 6x
and then 5y 1 4y
Factorising
Factorise fully:
a 6x2 2 3x
b 7x2 1 14xy
a 6x2 2 3x 5 3x(2x 2 1)
3 323 x 3x1 3 3 x
The 3 and the x are common.
b 7x2 1 14xy 5 7x(x 1 2y)
Take out the common 7x and
put in the bracket what is left.
Always check to see if when you expand the answer you get back to the start.
E.g. in your head expand 7x(x 1 2y) 5 7x2 1 14xy Yes!
Unit 2 | 13 Index notation, BIDMAS and further factorising | Student Book chapter 8
Now try these
39
Questions on this spread are targeted at the grades indicated.
F
1 Work out:
a 24 4 4 1 2
b 8 1 2 3 5
c (23 2 3) 4 (4 1 6)
d 7 1 3 3 2 1 4
e 9 2 (6 1 2)
f 15 4 (3 1 2)
g (6 2 1)2
h 6 1 9 4 3
i 24 4 (3 3 2)
E
2 Insert brackets into the following to make each statement true:
a 3 1 6 4 2 1 7 5 13
b 60 1 30 4 3 1 2 5 66
c 6 1 3 3 7 2 4 5 27
d 56 2 16 4 4 3 2 5 20
D
3 Penny says that 7(2x 2 3) 5 14x 2 3
Explain why Penny is incorrect.
C
4 Simplify these expressions by writing as a single power:
a 75 3 74
b 912 4 93
c 53 3 57 4 52
d 69 4 6
e 310 4 35
f 824 3 8
g 220 4 24
h 49 4 43 3 42
5 Simplify the following:
a a7 3 a3
b b8 4 b2
c c 3 c7 4 c2
d d15 4 d5
e e9 4 e3
f f 9 3 f 3 f 2
g g24 4 g4
h h14 4 h2 3 h3
3
k5 
i ______
​ k 32 ​
 
k
m20    
j ​ _______
​
4
m 3m
n7 3 n8 
k ​ _______
 ​
n3 3 n2
p 3 p9
l ​ ______
 ​ 
 
p3
6 Simplify the following:
a 4a8 3 3a7
b 12b7 4 3b2
c 5c5 3 6c6 4 3c3
d 9d18 4 3d6
e (3e8)3
g (7g6)2
30h18  ​ 
h ​ ________
2h 3 3h2
2f 5 3 6f 10
f _________
​ 
 ​ 
 
4f 3
7 Expand:
a a(a 1 5)
b b(7 2 2b)
c c(3c 1 1)
d 2d(7 2 d)
e 5e(4e 1 9)
f 6f(4 2 7f)
8 Expand and simplify:
a 4(a 1 5) 1 2(3a 1 7)
b 9(2b 1 5) 2 3(6b 1 3)
c 8(6 1 c) 2 6(1 2 2c)
d 7(8d 2 1) 1 2(9 2 2d)
e 5(9e 2 2) 2 10(6e 2 1)
9 Factorise fully:
a 8a 1 2
b 9 2 3b
d 10 1 15d
e ef 1 3e
g k 1 7k
h 3m 2 m i 8n2 1 2n
j 9p 2 15p2
k 7q2r 1 14qr
l t2u2 2 5tu
2
c 6c 2 12
f 8g 2 3gh
2